{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "bd051cef-64a1-4df9-9431-cc2f9f87ffa7",
   "metadata": {},
   "source": [
    "Ch25\n",
    "# 可视化正定性\n",
    "Book_1《编程不难》 | 鸢尾花书：从加减乘除到机器学习  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "764bd4fa-8439-48e9-aada-ce9499c3353c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 导入包\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sympy import symbols, lambdify, expand, simplify\n",
    "\n",
    "# 定义可视化函数\n",
    "def visualize(xx1,xx2,f2_array):\n",
    "    \n",
    "    fig = plt.figure(figsize=(6,3))\n",
    "    # 左子图，三维\n",
    "    ax_3D = fig.add_subplot(1, 2, 1, projection='3d')\n",
    "\n",
    "    ax_3D.plot_wireframe(xx1, xx2, f2_array, \n",
    "                         rstride=10, cstride=10,\n",
    "                         color = [0.8,0.8,0.8],\n",
    "                         linewidth = 0.25)\n",
    "\n",
    "    ax_3D.contour(xx1, xx2, f2_array, \n",
    "                  levels = 12, cmap = 'RdYlBu_r')\n",
    "\n",
    "    ax_3D.set_xlabel('$x_1$'); ax_3D.set_ylabel('$x_2$')\n",
    "    ax_3D.set_zlabel('$f(x_1,x_2)$')\n",
    "    ax_3D.set_proj_type('ortho')\n",
    "    ax_3D.set_xticks([]); ax_3D.set_yticks([])\n",
    "    ax_3D.set_zticks([])\n",
    "    ax_3D.view_init(azim=-120, elev=30)\n",
    "    ax_3D.grid(False)\n",
    "    ax_3D.set_xlim(xx1.min(), xx1.max()); \n",
    "    ax_3D.set_ylim(xx2.min(), xx2.max())\n",
    "    \n",
    "    # 右子图，平面等高线\n",
    "    ax_2D = fig.add_subplot(1, 2, 2)\n",
    "    ax_2D.contour(xx1, xx2, f2_array, \n",
    "                  levels = 12, cmap = 'RdYlBu_r')\n",
    "\n",
    "    ax_2D.set_xlabel('$x_1$'); ax_2D.set_ylabel('$x_2$')\n",
    "    ax_2D.set_xticks([]); ax_2D.set_yticks([])\n",
    "    ax_2D.set_aspect('equal'); ax_2D.grid(False)\n",
    "    ax_2D.set_xlim(xx1.min(), xx1.max()); \n",
    "    ax_2D.set_ylim(xx2.min(), xx2.max())\n",
    "    plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "67c7be41-b1d9-440e-a4d6-adab7168ba5b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2*x1*x2\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 生成数据\n",
    "x1_array = np.linspace(-2,2,201)\n",
    "x2_array = np.linspace(-2,2,201)\n",
    "\n",
    "xx1, xx2 = np.meshgrid(x1_array, x2_array)\n",
    "\n",
    "# 定义二元函数\n",
    "\n",
    "def fcn(A, xx1, xx2):\n",
    "\n",
    "    x1,x2 = symbols('x1 x2')\n",
    "    x = np.array([[x1,x2]]).T\n",
    "    f_x = x.T@A@x\n",
    "    f_x = f_x[0][0]\n",
    "    print(simplify(expand(f_x)))\n",
    "\n",
    "    f_x_fcn = lambdify([x1,x2],f_x)\n",
    "    ff_x = f_x_fcn(xx1,xx2)\n",
    "    \n",
    "    return ff_x\n",
    "    \n",
    "# 不定矩阵\n",
    "A = np.array([[0, 1],\n",
    "              [1, 0]])\n",
    "\n",
    "f2_array = fcn(A, xx1, xx2)\n",
    "visualize(xx1,xx2,f2_array)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
